Shmyr was one of the top defensive stars in the short history of the WHA, noted for his hard-nosed play, having jumped from the NHL's California Golden Seals to the upstart Cleveland Crusaders.

He subsequently played for the WHA's San Diego Mariners, where he enjoyed his best offensive campaign, and played two years for the Edmonton Oilers, captaining the club to a regular season league championship in the WHA's final season.

While the Stars' captain, he led them to a semifinal appearance in 1980 and to the 1981 Stanley Cup Finals, where they lost to the New York Islanders.

He finished third in the WHA's career leaders for games played, twentieth in assists, and fourth in penalty minutes.

[3] In 2010, he was elected as an inaugural inductee into the World Hockey Association Hall of Fame.